Preheat oven to 450 degrees. Place each chicken breast between two sheets of waxed paper, and pound to 1/4-inch thick. Season lightly with salt and pepper. Set aside.

In a medium skillet over medium heat, melt butter. Sauté onion and broccoli for approximately 5 minutes. Remove from heat. Stir in 1 cup of the cheese and the nutmeg. Place equal amounts of mixture in the center of each chicken breast. Fold edges of chicken over to cover stuffing mixture. Place breast, seam-side down, in a lightly greased baking dish. Sprinkle with the remaining mixture and 1/2 cup cheese. Top with paprika, if desired. Bake 12 to 15 minutes, until meat is cooked.